Question

The number of solutions of the system of equations $ x-y+z=2 $ $ 2x+y-z=5 $ $ 4x+y+z=10 $ is

• A. $ \infty $
• B. $ 1 $
• C. $ 2 $
• D. $ 0 $

Answer 1

Answer: (B)

Given system of equations are
$ x-y+z=2 $ $ 2x+y-z=5 $ and $ 4x+y+z=10 $
Now, $ A=\left| \begin{matrix} 1 & -1 & 1 \\ 2 & 1 & -1 \\ 4 & 1 & 1 \\ \end{matrix} \right| $
$ =1(1+1)+1(2+4)+1(2-4) $
$ =2+6-2 $ $ =6\ne 0 $
Hence, it has unique solution.b